Simple Interest
Math MCQs

Question :    Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $7480 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $5500

Rate of Simple Interest (R) = 6% per annum

Amount (A) = $7480

Thus, time (T) = ?

Method (1) Using Formula

Calculation of Simple Interest, when Principal and Amount are given

Formual to Calculate Simple Interest when Principal and Amount are given

We know that, Amount (A) = Principal (P) + Simple Interest (SI)

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $7480 – $5500 = $1980

Thus, Simple Interest = $1980

Calculation of the Time using forumula when Amount, Simple Interest and Principal are known

Formula to find the Time (T)

Time (T) = ^{100 × Simple Interest}/_{Principal × Rate of Interest}

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 1980}/_{5500 × 6}

= ¹⁹⁸⁰⁰⁰/₃₃₀₀₀

= 6 years (using formula)

Thus, Time (T) = 6 years (from time taken before calculation)Answer

Calculation of the Time using Unitary Method when Amount, Simple Interest and Principal are known

Here, we have

Principal (P) = $5500

Rate of Simple Interest (R) = 6% per annum

Simple Interest = $1980 (As calculated above by subtracting Principal from the Amount given)

We know that, interest is calculated on the basis of the Principal.

This means Simple Interest for 1 year = Rate of simple interest × Principal

Thus, Simple Interest for 1 year = 6% of Principal

= 6% of $5500

= ⁶/₁₀₀ × 5500

= ^{6 × 5500}/₁₀₀

= ³³⁰⁰⁰/₁₀₀ = 330

Thus, simple Interest for 1 year = $330

Now,

∵ If the simple Interest is $330, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₃₀ years

∴ If the simple Interest is $1980, then the time = ¹/₃₃₀ × 1980 years

= ^{1 × 1980}/₃₃₀ years

= ¹⁹⁸⁰/₃₃₀ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $9943 to clear the loan, then find the time period of the loan.

(2) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $10260 to clear the loan, then find the time period of the loan.

(3) How much loan did Joseph borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7125 to clear it?

(4) What amount does James have to pay after 5 years if he takes a loan of $3000 at 8% simple interest?

(5) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $8772 to clear the loan, then find the time period of the loan.

(6) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 10% simple interest?

(7) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6037.5 to clear it?

(8) In how much time a principal of $3000 will amount to $3750 at a simple interest of 5% per annum?

(9) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 9% simple interest.

(10) What amount does William have to pay after 6 years if he takes a loan of $3500 at 7% simple interest?